CS 5643: Physically Based Animation for Computer Graphics
Spring 2015


PROFESSOR:  Doug James

TA: Timothy Langlois (Office hours: Mon, 6-7pm, Gates G11)

HELP SESSIONS AND OFFICE HOURS:  After class, and by appointment. Please also ask questions on the Piazza forum.

DESCRIPTION:  Modern computer animation and interactive digital entertainment are making increasingly sophisticated use of tools from scientific and engineering computing. This course introduces students to common physically based modeling techniques for animation of virtual characters, fluids and gases, rigid and deformable solids, and other systems. Aspects of interactive simulation and multi-sensory feedback will also be discussed.  A hands-on programming approach will be taken, with an emphasis on small interactive computer programs.

TIME:  TR 2:55-4:10pm

LOCATION:  Gates G01

   
SCHEDULE (previous years: Spring 2013, Spring 2014)
DATE
TOPICS
SUPPLEMENTAL MATERIALS
ThJan22 Introduction

Readings:
  • An interesting historical perspective:
    • Terzopoulos, D., Platt, J., Barr, A., Zeltzer, D., Witkin, A., and Blinn, J. 1989. Physically based modeling: past, present, and future. In ACM SIGGRAPH 89 Panel Proceedings (Boston, Massachusetts, United States, July 31 - August 04, 1989). SIGGRAPH '89. ACM Press, New York, NY, 191-209. 
TuJan27 Particle Systems
Material:
ThJan29
Review: Tensor Calculus

Discussed differentiating the following quantities with respect to particle position vectors, p_i:
  • constant, c
  • position, p_j
  • vectors, (p_j-p_k)
  • distances, ||p_j-p_k||
  • distance powers, ||p_j-p_k||^n
  • functions of distance, W(||p_j-p_k||)
  • dot products, (p_1-p_0)^T (p_3-p_2)
  • cross products
  • Example: hair bending energy derivative, E = k*sin^2(theta/2)  [handout]
Other topics:
TuFeb03
ThFeb05
Constrained Dynamics
Material:
  • Holonomic constraints, C(p)=0.
  • Example: Bead on a wire
  • Differentiating constraints w.r.t. time.
  • Constraint Jacobian, J
  • Lagrange multipliers, lambda, and constraint forces, J^T lambda
  • Solving for Lagrange multipliers
  • (Implicit constraint (and half-explicit) DAE integration schemes)
  • Post-step projection schemes
    • Position- vs velocity-based corrections
  • Applications: Mechanical linkages, inextensibility constraints, incompressible flow, contact constraints
Written Homework (Due Thurs Feb 12)
References:
[Advanced] References for Differential-Algebraic Equations (DAEs):
TuFeb10
ThFeb12
Particle-based Fluids



Material:
ThFeb12 Assignment #1:
Position Based Fluids

Project webpage. Starter code is on CMS.
TuFeb17
Winter Break
No class
ThFeb19
Basic Integrators

Material:
  • Forward Euler
  • Backward Euler
  • Symplectic Euler (a.k.a. semi-implicit Euler); symplectic Euler adjoint
    • E. Hairer, C. Lubich, and G. Wanner. Geometric Numerical Integration. Structure-Preserving Algorithms for Ordinary Differential Equations., Springer Series in Comput. Mathematics, Springer-Verlag, volume 31, 2002.
  • Midpoint method
  • Verlet method (a.k.a. Störmer's method)
  • Stability analysis of forward & backward Euler schemes on test problem
TuFeb24
ThFeb26
Implicit Integration;
IMEX and other schemes

Material:
ThFeb26
TuMar03
ThMar05
Position Based Dynamics,
and other relaxation-based dynamics

References:

Assignment #2:
Position Based Dynamics

Project webpage. Starter code on CMS.
ThMar05
TuMar10
Robust Collision Processing
Material:
  • Motivation: cloth and hair animation
  • Continuous collision detection
    • 2D/3D sphere-sphere, 2D (point-edge), and 3D (point-face, edge-edge) tests
  • Velocity-level collision resolution; collision impulses
  • Supporting pin/trajectory constraints
    • Inverse-mass-matrix filtering
  • Penalty forces
  • Rigid cloth zones
  • Untangling cloth
References:
TuMar10
ThMar19
Rigid Body Simulation
Material:
  • Rigid body dynamics
    • Position, orientation, linear/angular velocity, momentum, inertia, equations of motion, etc.
    • Euler's equations of angular rigid-body dynamics (in body coordinates)
  • Contact impulses
  • Example: "rigid damping"
  • Frictionless contacts:
    • Nonpenetration constraints
    • Velocity-level constraints (see Baraff course notes for acceleration-level constraints)
    • Linear Complementarity Problem (LCP)
References:
ThMar12
TuMar17
Rigid Body Sound
Guest Lecturer: Tim Langlois

Material:
  • Modal sound synthesis
  • Precomputed acoustic transfer
  • Precomputed acceleration noise
  • Compression techniques
References:

ThMar19
...
Rigid Body Contact:
Impulse- and Constraint-based Methods


Material:
TuMar24 Final Project Idea Blitz!
A whirlwind discussion of ideas and paper references to inspire your final project choice.
ThMar26
Project working class

Working meeting to discuss A2-Part II (due FriMar27) and final project ideas with Tim Langlois (TA).
  • No lecture.
  • Prof James away--chairing SIGGRAPH 2015 Technical Papers committee meeting in Chicago.

TuApr07
ThApr09
Fluid Animation
Materials:
Reading
The Conjugate Gradient Method
Material:
  • Jonathan Richard Shewchuk, An Introduction to the Conjugate Gradient Method Without the Agonizing Pain, August 1994.  PDF (516k, 58 pages)
  • G.H. Golub and C.F. Van Loan, Matrix Computations, 4th Edition, Johns Hopkins University Press, 2013.
TuApr14
Shape Matching Methods
Material:
  • Matthias Müller, Bruno Heidelberger, Matthias Teschner, Markus Gross, Meshless deformations based on shape matching, ACM Transactions on Graphics, 24(3), August 2005, pp. 471-478. [ACM] [PDF] [AVI]
  • Alec R. Rivers, Doug L. James, FastLSM: Fast Lattice Shape Matching for Robust Real-Time Deformation, ACM Transactions on Graphics, 26(3), July 2007, pp. 82:1-82:6. [ACM] [PDF]
  • Denis Steinemann, Miguel A. Otaduy, Markus Gross, Fast Adaptive Shape Matching Deformations, ACM SIGGRAPH/Eurographics Symposium on Computer Animation, Dublin, July 7-9, 2008. [PDF] [AVI]
  • Matthias Müller and Nuttapong Chentanez. Solid simulation with oriented particles. ACM Trans. Graph. 30, 4, Article 92 (July 2011), 10 pages, 2011. [ACM] [PDF] [MOVIE]
ThApr16
Fracture Animation

Material:

TuApr21
Controlling Smoke, Water, & Fire
Materials:
ThApr23 Noise & Turbulence Modeling
from [Kim et al. 2008]
Materials:
TuApr28 Animation Sound



Material:
ThApr30
TuMay05
Project Presentations

Two-day extended in-class slide presentation period.
  • Give overview of animation problem
  • Demo preliminary results
  • Final project submitted on CMS by May 18

Presentation schedule (5 minute talks, randomized order):

Thursday, April 30 Speakers:

  1. Benton, Brandon 
  2. Wu, Rundong
  3. Zhang, Zechen   
  4. Rogers, Machenzie   
  5. Jiang, Mingde   
  6. Zhao, Zeqiang   
  7. Wang, Ning    
  8. Gross, Joel & Cytryn, Jeremy   
  9. Hakobyan, Gagik   
  10. Wu, Scott    
  11. Westura, Travis    

Tuesday, May 5 Speakers:

  1. Bern, Noah   
  2. Wang, Jui-hsien   
  3. Veizaga, Einar & Henderson, Kylar   
  4. Adegunloye, Olufemi   
  5. Peele, Bryan   
  6. Qian, Yuhao Collin   
  7. Evans, Bryce & Paris, Youenn   
  8. Sperling, Daniel   
  9. Duffany, Brandon    
  10. Dupre, Guillaume   









SUPPLEMENTAL MATERIAL

TOPICS
SUPPLEMENTAL MATERIALS
Deformable Models; and
Corotational Finite Elements

Material:
  • Blackboard
    • Basic continuum mechanics
      • Deformation (material and deformed coordinates, deformation gradient)
      • Polar decomposition (rotation, stretch)
      • Strain (Green, linearized Cauchy)
      • Strain Energy
      • Stress and forces
    • Tetrahedral finite elements
    • Corotational finite elements
  • References:


Assignment #1
Particle Systems


  Assignment #1 Homepage


Assignment #2
Robust Collision Processing
(a.k.a. "The Spaghetti Factory")
Assignment #2 Homepage
  • Video highlights (from previous years):

Solving Sparse Linear Systems

Material:

Assignment #3
Rigid Body Contact
(a.k.a. "The Jelly Bean Factory")
Material:
  • Starter code available from CMS 




Fluid-Solid Coupling
Materials:

Passive Rigid Motion Control


Material:
  • Simulation accuracy vs plausibility
  • Exploiting errors for control
    • Random sampling methods
    • Optimization based methods
    • Interactive artist-driven methods
References: